We study the ground states and left-excited states of the A k−1 N = (2, 0) little string theory. Via a theorem by Atiyah [1], these sectors can be captured by a supersymmetric nonlinear sigma model on CP 1 with target space the based loop group of SU (k). The ground states, described by L 2 -cohomology classes, form modules over an affine Lie algebra, while the left-excited states, described by chiral differential operators, form modules over a toroidal Lie algebra. We also apply our results to analyze the 1/2 and 1/4 BPS sectors of the M5-brane worldvolume theory.In loving memory of See-Hong Tan.